Add these two fractions: [tex]$\frac{1}{6}+\frac{3}{5}=?$[/tex]
Answer (2)
Find the least common denominator (LCD) of 6 and 5, which is 30.
Rewrite the fractions with the LCD: 6 1 = 30 5 and 5 3 = 30 18 .
Add the fractions: 30 5 + 30 18 = 30 23 .
The final answer is 30 23 .
Explanation
Finding a Common Denominator We need to add two fractions, 6 1 and 5 3 . To do this, we first need to find a common denominator. The least common denominator (LCD) is the smallest multiple that both denominators (6 and 5) share.
Determining the LCD The least common denominator of 6 and 5 is 30. We can find this by listing the multiples of each number until we find a common one: Multiples of 6: 6, 12, 18, 24, 30, 36, ... Multiples of 5: 5, 10, 15, 20, 25, 30, 35, ... The smallest multiple they share is 30.
Rewriting Fractions Now, we rewrite each fraction with the common denominator of 30: 6 1 = 6 × 5 1 × 5 = 30 5 5 3 = 5 × 6 3 × 6 = 30 18
Adding the Fractions Now that both fractions have the same denominator, we can add them: 30 5 + 30 18 = 30 5 + 18 = 30 23
Simplifying the Result The resulting fraction is 30 23 . We check if this fraction can be simplified. Since 23 is a prime number and does not divide 30, the fraction is already in its simplest form.
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. Understanding how to add fractions is essential for accurate calculations in these situations. For example, if you need 6 1 of a cup of flour and 5 3 of a cup of sugar for a recipe, adding these fractions helps you determine the total amount of dry ingredients needed: 6 1 + 5 3 = 30 23 of a cup.
To add 6 1 and 5 3 , we find a common denominator of 30. We rewrite the fractions as 30 5 and 30 18 , and then add them together, resulting in 30 23 . The final answer is 30 23 .
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